A simpler expression can be obtained for \(\theta _r\)  by applying the theory of deterministic equivalents to not just the channel norms but also to the interference.
Thus, \(|\mathbf {h}_i^H \mathbf {h}_m|^2/N \stackrel{\text{a.s.}}{\longrightarrow } \sigma _h^4\) , as \(N \rightarrow \infty \)  [1]}.
Thus, the SINR becomes
\({\rho }^k_{m} &= N/(\rho _0^{-1} + r-k),\) 
